Pradana, Yona Lotusia (2019) Kontrol Optimal Model Penyebaran Penyakit Rabie. Sarjana thesis, Universitas Brawijaya.
Abstract
Pada skripsi ini dibahas model penyebaran penyakit rabies dengan kontrol pre-exposure prophylaxis dan post-exposure prophylaxis. Analisis dinamik yang dilakukan pada model meliputi penentuan titik kesetimbangan, angka reproduksi dasar (ℛ0), dan analisis kestabilan lokal. Berdasarkan hasil analisis diperoleh dua titik kesetimbangan, yaitu titik kesetimbangan bebas penyakit dan titik kesetimbangan endemik. Titik kesetimbangan bebas penyakit rabies selalu eksis, sedangkan titik kesetimbangan endemik eksis ketika ℛ 0 > 1. Titik kesetimbangan bebas penyakit bersifat stabil asimtotik lokal jika ℛ0 < 1, sedangkan titik kesetimbangan endemik bersifat stabil asimtotik lokal jika memenuhi kriteria Routh-Hurwitz. Ketika ℛ 0 > 1, maka terjadi penyebaran penyakit rabies sehingga dilakukan kontrol optimal pada model. Tujuan pemberian kontrol ini untuk meminimumkan kepadatan subpopulasi terpapar dan terinfeksi virus rabies. Masalah kontrol optimal diselesaikan dengan menerapkan prinsip minimum Pontryagin dan simulasi numerik dilakukan menggunakan metode Sweep Maju-Mundur. Hasil simulasi numerik menunjukkan bahwa pemberian kontrol pre-exposure prophylaxis dan post-exposure prophylaxis secara bersamaan dapat meminimumkan kepadatan subpopulasi terpapar dan terinfeksi virus rabies secara signifika
English Abstract
This final project discussed optimal control on rabies epidemic model with control pre-exposure prophylaxis and postexposure prophylaxis. Dynamical analysis includes the determination of equilibrium point, the basic reproduction number (ℛ0), and the local stability analysis. Based on the analytical results, two equilibrium points are obtained, namely disease free equilibrium point and endemic equilibrium point. The rabies-free equilibrium always exist, while the endemic equilibrium exist when ℛ0 > 1. The disease free equilibrium is local asymptotically stable when ℛ0 < 1, while the endemic equilibrium point is local asymptotically stable if it satisfies the Routh-Hurwitz criteria. When ℛ 0 > 1, the spread of rabies needs the application of control on the model. The purpose of this control is to minimize the density of exposed and infected subpopulations. The optimal control problem is solved using Pontryagin minimum principle, while the numerical simulation is done by applying Forward-Backward Sweep method. The result of numerical simulation shows that the control of pre-exposure prophylaxis and post-exposure prophylaxis can minimize the density of the exposed and infected subpopulation significantly
Other obstract
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| Item Type: | Thesis (Sarjana) |
|---|---|
| Identification Number: | SKR/MIPA/2019/505/052001662 |
| Uncontrolled Keywords: | model penyebaran penyakit rabies, vaksin, pengobatan, analisis kestabilan, kontrol optimal, model of the spread of rabies, vaccine, treatment, stability analysis, optimal control. |
| Subjects: | 500 Natural sciences and mathematics > 519 Probabilities and applied mathematics > 519.6 Mathematical optimization |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika |
| Depositing User: | Budi Wahyono Wahyono |
| Date Deposited: | 10 Aug 2020 07:43 |
| Last Modified: | 10 Aug 2020 07:43 |
| URI: | http://repository.ub.ac.id/id/eprint/178930 |
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